I don't think the LabelClass—Help | ArcGIS Desktop provides access to set the field used for labeling a layer. If that is the case, you could create layerfiles with the appropriate label settings and apply these layerfiles for the different maps using UpdateLayer—Help | ArcGIS Desktop . Or duplicate the layer in your TOC with the different label settings and switch them on and off depending on the map using the visible property of the Layer—Help | ArcGIS Desktop .

The LabelClass object does provide access to change the field through the expression property. When the label class is 'Default', the expression is simply the name of the field to label. If the user updates the expression to a different field and refresh the active view, the labels get updated.